A) 1
B) \[\sqrt{2}\]
C) \[\sqrt{3}\]
D) 2
Correct Answer: A
Solution :
\[\frac{1}{1+\sqrt{2}+\sqrt{3}}+\frac{1}{1-\sqrt{2}+\sqrt{3}}\] \[=\frac{1+\sqrt{3}-\sqrt{2}+1+\sqrt{2}+\sqrt{3}}{9(1+\sqrt{3})+(\sqrt{2})\,((1+\sqrt{3})-\sqrt{2})}\] \[=\frac{2(1+\sqrt{3})}{{{(1+\sqrt{3})}^{2}}-{{(\sqrt{2})}^{2}}}=\frac{2(1+\sqrt{3})}{1+3+2\sqrt{3}-2}\] \[=\frac{2(1+\sqrt{3})}{2(1+\sqrt{3})}=\]
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